@Article{Malejki2010,
author = "Malejki, Maria",
title = "Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "3",
pages = "311--330",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.3.311",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.3.311",
abstract = "The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from \(1\) to \(N\), for a Jacobi matrix \(J\) by the eigenvalues of the finite submatrix \(J_n\) of order \(pn \times pn\), where \(N = \max \{k \in \mathbb{N}: k \leq rpn\}\) and \(r \in (0,1)\) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of \(J\) in the case \(p=3\).",
keywords = "symmetric unbounded Jacobi matrix, block Jacobi matrix, tridiagonal matrix, point spectrum, eigenvalue, asymptotics",
issn = "1232-9274"
}